Are ditch networks optimised for mitigating rill erosion in cultivated Mediterranean landscapes? A numerical experiment

Rill erosion frequently occurs in Mediterranean cultivated landscapes due to high rainfall intensities, low soil organic matter concentrations and low vegetation coverage. Among other rill erosion mitigation practices, farmers have historically built ditch networks to intercept runoff upstream of cultivated plots. However, the construction and maintenance of these ditches generate indirect costs for farmers and land managers. Therefore, a compromise must be found between these costs and the efficiency of the ditch network for mitigating erosion. Thus, tools and methods are required for determining an optimised cost-efficient compromise or for diagnosing existing ditch networks. This paper proposes an experimental approach to test in silico how well an actual soil conservation practice (i.e., a ditch network) reaches a costefficiency compromise at the catchment scale. The costs are approximated from the density of the ditches, and the rill erosion mitigation efficiency is summarised using an aggregated modified stream power index. The actual ditch network is compared to a set of virtual ditch networks that are generated by a stochastic network simulator that optimises the network geometries with regard to preventing rill erosion. This approach was applied in four small vineyard subcatchments located in the Peyne catchment in Languedoc, southern France. Actual ditch networks are compared to virtual networks, which present a large range of ditch network densities. The ditch network highly mitigates rill erosion because the Stream Power Index (SPI) values exponentially decrease with the ditch network density and because the actual SPI maps are homogeneous. In addition, the results from the four different sub-catchments indicated that the rill erosion risk was mitigated by using minimal drainage network lengths, which suggested that the actual ditch networks that resulted from historical farmers were optimised. The proposed approach can be used to determine if the efficiency of ditch networks for mitigating erosion can be improved.